Predicting fall risk using multiple mechanics-based metrics for a planar biped model

by Daniel Williams, Anne E. Martin

For both humans and robots, falls are undesirable, motivating the development of fall prediction models. Many mechanics-based fall risk metrics have been proposed and validated to varying degrees, including the extrapolated center of mass, the foot rotation index, Lyapunov exponents, joint and spatiotemporal variability, and mean spatiotemporal parameters. To obtain a best-case estimate of how well these metrics can predict fall risk both individually and in combination, this work used a planar six-link hip-knee-ankle biped model with curved feet walking at speeds ranging from 0.8 m/s to 1.2 m/s. The true number of steps to fall was determined using the mean first passage times from a Markov chain describing the gaits. In addition, each metric was estimated using the Markov chain of the gait. Because calculating the fall risk metrics from the Markov chain had not been done before, the results were validated using brute force simulations. Except for the short-term Lyapunov exponents, the Markov chains could accurately calculate the metrics. Using the Markov chain data, quadratic fall prediction models were created and evaluated. The models were further evaluated using differing length brute force simulations. None of the 49 tested fall risk metrics could accurately predict the number of steps to fall by themselves. However, when all the fall risk metrics except the Lyapunov exponents were combined into a single model, the accuracy increased substantially. These results suggest that multiple fall risk metrics must be combined to obtain a useful measure of stability. As expected, as the number of steps used to calculate the fall risk metrics increased, the accuracy and precision increased. This led to a corresponding increase in the accuracy and precision of the combined fall risk model. 300 step simulations seemed to provide the best tradeoff between accuracy and using as few steps as possible.